On the arcade (or NES VS. System, to some) release of VS. Super Mario Bros., you can continue after having a game over. When you lose all of your lives, hold the A Button at the title screen, then press Start to start again from the last played world. Level progress is not saved, however: for example, having a game over on World 4-4 and using this trick brings you back to World 4-1.
Timer Underflow Glitch
This glitch only works in the castle levels where you fight Bowser at the end - for example, World 1-4, 2-4, 3-4, and so on. It is best to defeat Bowser with Fire Mario or Fire Luigi beforehand, as you must wait out most of the timer to execute this glitch. At the end of the castle levels, there is an axe which you must touch to end the level. If you time your jump correctly (a full jump as the timer goes from 002 to 001 often works) and land on the axe while the timer reads "000", you'll continue as normal to the usual sequence at the end of the castle. However, your timer bonus (50 points per second remaining) will be calculated as if you had 999 seconds, not zero, left on the clock. This allows for an easy 49,950 point boost! Note that this glitch, if executed on levels using a flagpole, will prevent you from earning the bonus in that level.
Warp to World 5
In World 4-2, near the end of the underground segment, you will have to pass over a pipe with a Piranha Plant in it. Instead, you can use Big/Fire Mario/Luigi to break the blocks above it and go right and along the path to a warp zone. (Alternately, you can use an earlier elevator to get on the roof and get here.) The warp is to World 5.
Warp to World 6
In World 4-2, as you head right in the underground segment, you will see seven ? Blocks (2 over 2, with 3 to the side). Past the next gap are some blocks on the roof. You can bounce around near here to reveal some blocks, which you can use to hit the already-revealed bricks to reveal a vine. Climb this vine to go up and into a linear platforming area leading to a warp zone, which takes you to World 6.
Warp to Worlds 2, 3, or 4
In World 1-2, you will find some elevators near the end of the underground segment. You can use these to ride onto the blocks making up the roof, then go right and past the warp pipe you're normally supposed to take outside. This will bring you to a warp zone that can bring you to Worlds 2, 3, or 4.